Mathematical modelling of thin layer drying process of long green pepper in solar dryer and under open sun

An experimental study was performed to determine the thin layer drying characteristics in a solar dryer with forced convection and under open sun with natural convection of long green pepper. An indirect forced convection solar dryer consisting of a solar air collector and drying cabinet was used in the experiments. Natural sun drying experiments were conducted for comparison at the same time. The constant rate period is absent from the drying curves. The drying process took place in the falling rate period. The drying data were fitted to 13 different mathematical models. Among the models, the logarithmic model for forced solar drying and the Midilli and Kucuk model for natural sun drying were found best to explain the thin layer drying behaviour of long green peppers. The performance of these models was investigated by comparing the coefficient of determination (R), reduced chi-square (χ²) and root mean square error (RMSE) between the observed and predicted moisture ratios.     

Estimation of moisture content in timber using ultrasonics

This paper presents the findings of a research programme on the estimation of moisture content in timber using ultrasonics, by developing working relationships between ultrasonic wave velocity, temperature and percentage moisture content in timber samples during kiln drying. A detailed experimental programme was undertaken to develop relationships between ultrasonic wave propagation velocity and temperature, and between velocity and percentage moisture content for a large number of timber samples. The experimental programme was primarily restricted to samples of jarrah timber, but the procedures can be applied to other species.

The results show conclusively that both temperature and moisture content have a significant effect on the ultrasonic wave propagation velocity in timber, whereas material density does not. Thus, ultrasonics can be used to monitor variations in percentage moisture content during the drying process in a kiln environment.

A simple field-testing procedure has been developed for monitoring moisture content in timber using ultrasonics either manually (with a hand calculator) or incorporated into a computer program for on-line monitoring. The procedure is based on simple quadratic equations derived from a statistical regression analysis of velocity and temperature relationships, and velocity and percentage moisture-content relationships. To overcome any measurement inaccuracies due to density variations or other factors, the recommended procedure involves the initial calibration of each sample board.     

A steady-state model for the forced convection solar cabinet dryer

The insufficient knowledge base for the design and optimization of solar dryer could be the obstacle to the unrealized promise of solar drying. By applying the lumped-parameter approach in the analysis of the transfer processes and utilizing known results from drying theory, this article demonstrates a methodology for the construction of a reduced mathematical model of the forced convection solar cabinet dryer. The model comprises only the variables directly involved in the energy and mass balance relationships for the drying process. The values of the variables determine the state of the processes in the dryer, and the model is a set of relationships that determines such a state. Specializing into thin product bed with sponge pieces constituting the product, this article describes an experiment carried out to verify the model. It also presents an assessment of the model parameter value from the experimental result and a simulation procedure with a result, which positively validates the model.The procedure used indentifies and quantifies the important mechanisms occurring in the solar drying process. This opens up a new dimension in the design and optimization of the solar dryer and the dryer operation. The article hopes to contribute towards the knowledge base and stimulate further interest in solar drying.     

A new termination control method for a clothes drying process in a clothes dryer

This paper reports on a study of developing a new termination control method for a clothes dryer, using both mathematical modeling and experimental approaches. Drying models in a constant-rate drying period (CRDP) and a falling-rate drying period (FRDP) were developed, based on well-established drying theory and using a “semi-empirical” approach. Drying experiments with regard to drying of cotton fabrics in different drying environments were carried out. A new termination control method using the equilibrium moisture content in ambient environment as a termination point has been investigated. The effectiveness of this new method has been evaluated by both experimental and modelling approaches. The results of the evaluation have demonstrated that the new method is workable and can help achieve energy saving.     

纸面石膏板干燥过程的分段解析与模拟

干燥工序是纸面石膏板生产过程中的关键环节之一。该干燥过程可分为加速干燥阶段、等速干燥阶段和降速干燥阶段。本文在一些合理的简化条件下，利用传输原理对纸面石膏板干燥过程的三个干燥阶段分别进行了解析，并对其进行了数值模拟，为纸面石膏板干燥过程的在线控制提供了依据。     

Farrington Daniels address, 1997 in the service of mankind

In the past 5 years the general attitude towards solar energy has turned from negative to positive. This in itself, however, will not accelerate the introduction of solar energy very much. On the contrary, some of the plans and programs following from it are unrealistic and counter-productive. The better way to go is realism and inspiring the best scientists and politicians to take up the vast amount of R&D work and societal restructuring that has still to be done. Energy has become so vital to mankind that solar energy as a substitute for conventional energy sources will be indispensable for maintaining peace.     

A simple moisture transfer model for drying of sliced foods

The mathematical formulation of mass transfer in drying processes is often based on the nonlinear unsteady diffusion equation. In general, numerical simulations are required to solve these equations. Very often, however, indirect and simplified methods neglecting fundamentals of the processes are used. In this work, a new mathematical model approach for the mass transfer occurring during drying of sliced foods is proposed. The model considers fundamentals of the drying process and takes internal resistance to moisture transfer into account. The parameters in the formulation have physical meaning and permit giving clear view of the moisture depletion process occurring during drying. The proposed model has an analytical solution and allows finding effective diffusion coefficient accurately. The verification of the model is made with basic drying experiments performed for chili red peppers sliced in slab form. The results reveal that there is nearly perfect match between the drying curves obtained by the model and the experiments.     

Mathematical Modeling of Heat and Mass Transfer during Convective Dehydration of an Anisotropic Cylindrical Foodstuff

Two‐dimensional, unsteady‐state mass transfer was studied for air drying of an anisotropic finite cylindrical body. A mathematical model was developed for predicting the temperature of the drying sample at any time and moisture in any position in the drying sample at any time. The anisotropic nature of the drying material was considered in the mathematical model by taking into account the different moisture diffusivities in the axial and radial directions. A cut fresh green bean was used as an anisotropic material and a pilot‐scaled dryer was set up to investigate the drying behavior of this foodstuff. Several length‐to‐diameter ratios of fresh green beans were considered and the mathematical model was validated by comparison of the predicted values of average moisture content with the experimental data. The model was used to predict the moisture distributions inside the drying samples. Different moisture content distributions in the axial and radial directions during drying confirms the anisotropic nature of cut green bean samples. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21119     

Modeling,simulation, and optimization of a microalgae biomass drying process

The aim of the present work was to develop a transient mathematical model focused on microalgae biomass drying, considering two phases: solid (wet biomass) and gas (drying air). Mass and thermal energy balances were written for each phase producing a system of ordinary differential equations (ODE). The solution of the ODE set delivers the temperature and air humidity ratio and biomass profiles with respect to time. The numerical results were directly compared with temperature experimental measurements—for both phases—and with the biomass humidity content. Data from experiment 1 were used to carry out the mathematical model adjustment, whereas data from experiment 2 were used for the experimental validation of the model. The model was adjusted by proposing a new correlation for the mass transfer coefficient and by calibrating the heat transfer coefficient. The transient numerical results were in good quantitative and qualitative agreement with the experimental results, ie, within the experimental error bars. Then the experimentally validated mathematical model was utilized to optimize the following parameters: (i) the electric heater power ( ) and the dry air mass flow rate ( ) and (ii) the convection oven length to width ratio (L/W). The goal was to minimize system energy consumption (objective function). The optimization procedure was subject to the following physical constraints: (i) fixed convection oven total volume and (ii) fixed biomass and drying air contact surface area. For the oven original geometry,  = 3.0 kW and  = 9 g s^?1 were numerically found for minimum energy consumption, so that 36.9% and 43.5% energy consumption decreases were obtained, respectively, in comparison with the measurements of experiment 1. Next, the numerical geometric optimization found (L/W)_opt = 9, with and , which was capable to reach a 51.6% energy consumption reduction in comparison with the original system tested in experiment 1. The novelty of this work consists of the development and experimental validation of a physically based microalgae biomass drying mathematical model, ie, instead of using empirical correlations to predict the drying time and temperature profiles and then minimize system energy consumption. Therefore, the results show that it is reasonable to state that the model could be used to design, control, and optimize drying systems with configurations similar to the one analyzed in this study.     

Mathematical modelling of the thin layer solar drying of banana, mango and cassava

The main objectives of this paper are firstly to investigate the behaviour of the thin layer drying of plantain banana, mango and cassava experimentally in a direct solar dryer and secondly to perform mathematical modelling by using thin layer drying models encountered in literature. The variation of the moisture content of the products studied and principal drying parameters are analysed. Seven statistical models, which are empirical or semi-empirical, are tested to validate the experimental data. A non-linear regression analysis using a statistical computer program is used to evaluate the constants of the models. The Henderson and Pabis drying model is found to be the most suitable for describing the solar drying curves of plantain banana, mango and cassava. The drying data of these products have been analysed to obtain the values of the effective diffusivity during the falling drying rate phase.     

Preparation,electrochemical performance and phase transition of high voltage LiNi0.5Mn1.5O4 cathode material

尖晶石LiNi_0.5Mn_1.5O₄因其可在4.7 V高电位下工作并有良好的循环特性,已成为最具潜力的高能量密度锂离子电池正极材料。本文首先采用喷雾干燥辅助烧结法制备了LiNi_0.5Mn_1.5O₄正极材料,考察了热处理条件对材料结构与性能的影响。用XRD、SEM和FT-IR等技术对所制备的LiNi_0.5Mn_1.5O₄材料的结构和表面形貌进行表征,利用原位XRD技术研究了LiNi_0.5Mn_1.5O₄正极材料在充放电过程中结构相变规律。结果表明,所制备的LiNi_0.5Mn_1.5O₄材料均具有Fd-3m空间群的立方相尖晶石型结构,并具有优异的电化学性能,其0.1 C时首次放电容量为132 mA·h/g,首轮库仑效率93.48%,高倍率下该材料的电化学性能优越。原位XRD测量结果分析表明,尖晶石型LiNi_0.5Mn_1.5O₄材料在充电过程中存在4个显著的相变过程,在嵌脱锂过程中,从四面体相向立方相结构相变过程是可逆的。     

Convective drying of food materials: An overview with fundamental aspect,recent developments,and summary

Convective drying is an ancient technique to dry moist materials. Many experimental and numerical studies on convective drying enriched the knowledge of researchers and industrialists for further research and developments. In this study, a thorough review is made on convective drying of food materials. A brief history of convective drying, its importance, methods, applications, and statistical data are clearly reviewed. The impact of important drying parameters such as shrinkage and influence of pretreatment during convective drying have been critically appraised. Instruments used, experimental setup developed, and properties measured and estimated have been listed and analyzed. A novel technology of taking snapshots during drying using the thermal camera is discussed. Different mathematical models such as analytical and numerical methods and its present challenges are extensively reviewed and discussed. An advanced level solution for convective drying at present is explained. Gaps in numerical methods to solve convective drying problems have been discussed and effective summaries are drawn.     

Thin layer convective solar drying and mathematical modeling of prickly pear peel (Opuntia ficus indica)

This paper presents the thin layer convective solar drying and mathematical modeling of prickly pear peel. For these purposes, an indirect forced convection solar dryer consisting of a solar air collector, an auxiliary heater, a circulation fan and a drying cabinet is used for drying experiments. Moreover, the prickly pear peel is sufficiently dried in the ranges of 32 to 36 °C of ambient air temperature, 50 to 60 °C of drying air temperature, 23 to 34% of relative humidity, 0.0277 to 0.0833 m³/s of drying air flow rate and 200 to 950 W/m² of daily solar radiation. The experimental drying curves show only a falling drying rate period. The main factor in controlling the drying rate was found to be the drying air temperature. The drying rate equation is determined empirically from the characteristic drying curve.Also, the experimental drying curves obtained were fitted to a number of mathematical models. The Midilli–Kucuk drying model was found to satisfactorily describe the solar drying curves of prickly pear peel with a correlation coefficient (r) of 0.9998 and chi-square (χ²) of 4.6572 10⁻⁵.     

Interrelationships between total, direct, and diffuse solar radiation in the tropics

Formulas that directly yield intensities of direct and diffuse radiation on horizontal surfaces from measurements of hourly total radiation only have been developed. Alternatively, atmospheric turbidity and solar altitude can also yield similar results. These formulas result in obtaining relations similar to those given by Parmelee from data collected in the United States. The data for New Delhi have also been shown to agree with these correlations.

Computed values of direct solar radiation on a horizontal surface or at normal incidence, are expressed by a mathematical expression that is shown to agree closely with the computed values obtained by Rao and Seshadri.

Correlation between hourly direct and total transmission factors has been shown to depend on the solar altitude, in addition to the atmospheric turbidity.     

A mathematical model for the spray freeze drying process: The drying of frozen particles in trays and in vials on trays

A mathematical model is presented that can be used to study the heat and mass transfer mechanisms that determine the dynamic behavior of the primary and secondary drying stages of spray freeze drying (freeze drying of particle based materials) in trays and in vials on trays. Simulation results indicate that particle based materials require longer primary drying times than solution based materials (conventional freeze drying) due to (a) reductions in the heat and mass transfer capabilities of particle based materials, and (b) the development of a secondary porous dried layer near the surface of the lower heating plate during the primary drying stage of the spray freeze drying process. The results of spray freeze drying for the systems studied in this work indicate that the drying rate during the primary drying stage increases as (i) the product height decreases, (ii) the particle diameter increases, and (iii) the value of the packing porosity increases. The mathematical model presented in this work is considered to offer a necessary and essential capability that could be used for the design, optimization, and control of the spray freeze drying process as well as of a process involving the drying of frozen particles in packed beds.     

Chemical storage of solar energy kinetics of heterogeneous SO3 and H2O reaction—Reaction analysis and reactor design

The first energy recovery step in the ammonium hydrogen sulfate (AHS) cycle is the formation of H₂SO₄(l) from H₂O(g) and SO₃(g). It has been determined that the optimum way to accomplish this is by the use of a double pipe tubular reactor. In this paper, a mathematical model for the reactor is presented, applied to the three reaction zones, and a method of numerical solution discussed. Three horizontal pilot-scale configurations, 0.234 × 10⁶ to 5.863 × 10⁶ kJ/h energy release, are discussed and sizing presented. Also, the results for a vertical configuration are presented. The need for additional work on two-phase gas-liquid flow in condensing systems and in annuli has been identified. The most important conclusion is that a high temperature can be achieved in the reactor by the use of a front end adiabatic section followed by nonadiabatic sections to recover the heat released.     

Investigation of a new solar greenhouse drying system for peppers

Solar drying is the oldest preservation technique of agricultural products using several types of solar crop dryers based mostly on solar energy, which is abundant, renewable and sustainable. This study aimed to modeling a new solar greenhouse drying system (SGDS) for the drying of red peppers. The proposed mixed-mode (SGDS) consists of two main parts, namely a flat plate solar air collector and an experimental greenhouse. A mathematical model is developed using the TRNSYS simulation program to predict the change in the drying kinetics during the drying process under our proposed (SGDS). The experimental part consisted in testing the solar air collector to investigate its performance. The test showed that this solar air collector has a good performance; its efficiency varies between 0, 5 and 0, 65. The model was validated with the observed data and showed good agreement with experimental values. The influence of the area of the product to be dried, airflow rate and collector area, on moisture content changes, air temperature and humidity inside the greenhouse was studied. For the case study of this SGDS, the results obtained from simulation showed that the optimum values of area of the product to be dried, the exhaust airflow rate and the collector area were found to be 40 m², 250 kg/h and 2 m², respectively.     

Optimal synthesis of heat-and-power systems: the operating line method

The physical and mathematical models on which the operating line method (OLM) (H. A. Irazoqui, Chem. Engng Sci. 41, 1243–1255 (1986); P. A. Aguirre, E. O. Pavani and H. A. Irazoqui, Chem. Engng Sci. 44, 803–816 (1989)) for the optimal synthesis of heat-and-power systems is built, are discussed in depth. These models include the heat exchange ‘modes’ allowed and the general features of the type of solution sought in order to reach an optimal scheme for the total energy systems in chemical plants. A thorough development of the mathematical technique used to tackle the optimization problem is also made. This development comprises the derivation of the necessary and sufficient conditions for optimality.